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Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.
Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and
Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a connected ne
We present an extension of the Lowdin strategy to find arbitrary matrix elements of generic Slater determinants. The new method applies to arbitrary number of fermionic operators, even in the case of a singular overlap matrix.
We report a cluster of results on k-QSAT, the problem of quantum satisfiability for k-qubit projectors which generalizes classical satisfiability with k-bit clauses to the quantum setting. First we define the NP-complete problem of product satisfiabi
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the area law. In this work, we